Burg Method (DSP Blockset)

Compute a parametric spectral estimate using the Burg method.

Library

Power Spectrum Estimation, in Estimation

Description

The Burg Method block estimates the power spectral density (PSD) of the input frame using the Burg method. This method fits an autoregressive (AR) model to the signal by minimizing (least-squares) the forward and backward prediction errors while constraining the AR parameters to satisfy the Levinson-Durbin recursion. The spectrum is then computed from the FFT of the estimated AR model parameters.

The order of the all-pole model is specified by the Order parameter. The Burg Method and Yule-Walker Method blocks return similar results for large frame sizes.

The input is a frame of consecutive time samples; a matrix input, u, is also treated as a single frame, u(:). The block's output is the estimate of the signal's power spectral density at N_fft equally spaced frequency points in the range [0,F_s), where N_fft is specified as a power of 2 by the FFT Size parameter and F_s is the signal's sample frequency. A value of -1 for FFT size instructs the block to use the input frame size as the FFT size. Otherwise, the block zero pads or truncates the input to N_fft before computing the FFT.

The following table compares the features of the Burg Method block to the Covariance Method, Modified Covariance Method, and Yule-Walker Method blocks.


	Burg	Covariance	Modified Covariance	Yule-Walker
Characteristics	Does not apply window to data	Does not apply window to data	Does not apply window to data	Applies window to data
	Minimizes the forward and backward prediction errors in the least-squares sense, with the AR coefficients constrained to satisfy the L-D recursion	Minimizes the forward prediction error in the least-squares sense	Minimizes the forward and backward prediction errors in the least-squares sense	Minimizes the forward prediction error in the least-squares sense (also called "Autocorrelation method")
Advantages	High resolution for short data records	Better resolution than Y-W for short data records (more accurate estimates)	High resolution for short data records	Performs as well as other methods for large data records
	Always produces a stable model	Able to extract frequencies from data consisting of p or more pure sinusoids	Able to extract frequencies from data consisting of p or more pure sinusoids	Always produces a stable model
			Does not suffer spectral line-splitting
Disadvantages	Peak locations highly dependent on initial phase	May produce unstable models	May produce unstable models	Performs relatively poorly for short data records
	May suffer spectral line-splitting for sinusoids in noise, or when order is very large	Frequency bias for estimates of sinusoids in noise	Peak locations slightly dependent on initial phase	Frequency bias for estimates of sinusoids in noise
	Frequency bias for estimates of sinusoids in noise		Minor frequency bias for estimates of sinusoids in noise
Conditions for Nonsingularity		Order must be less than or equal to half the input frame size	Order must be less than or equal to 2/3 the input frame size	Because of the biased estimate, the autocorrelation matrix is guaranteed to positive-definite, hence nonsingular

Dialog Box

FFT size: The number of samples on which to perform the FFT, N_fft. If N_fft exceeds the frame size, the data is zero padded as needed.
Order: The order of the AR model.

References

Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.

Orfanidis, J. S. Optimum Signal Processing: An Introduction. 2nd ed. New York, NY: Macmillan, 1985.